It is up to Corzine, a Democrat elected two weeks ago, to appoint someone to fill his Senate seat until next November's elections.
The senator has been mum about whom he might pick or when, but he has said he wants someone who can win an election next fall to keep the seat under Democratic control.
Codey's announcement opens the door wider for members of the state's congressional delegation who have expressed interest: Reps. Robert Menendez, Rob Andrews and Frank Pallone. Three other New Jersey congressmen are considered long shots for the job.
Menendez and Andrews have indicated they will run in 2006, even if Corzine chooses someone else to fill the remainder of his term.
Menendez has raised the most money for a 2006 Senate run, $4.1 million, compared to $2 million each raised by Pallone and Andrews. Menendez also has the support of the state's Hispanic community, who have been lobbying Corzine on the congressman's behalf. If appointed, he would be the second Cuban-American and third Hispanic in the Senate.
Corzine's transition team declined to comment Wednesday, and neither Codey nor the state Democratic organization would speculate on Corzine's choice.
Whomever Corzine picks will likely face Republican state Sen. Tom Kean Jr., in a general election in November.
Codey, who as the state Senate president succeeded Gov. James E. McGreevey after McGreevey resigned in a gay sex scandal a year ago, has enjoyed widespread popularity and was the apparent favorite among voters for the Senate seat.
But Codey said that going to Washington would disrupt life for both him and his wife. He said that when he informed his wife of his decision, he told her it was "an early anniversary present."
"She told me I was cheap," Codey said.
A Quinnipiac University poll released Tuesday showed 43 percent of voters thought Codey was the right man for the job. The runner-up was Menendez at 14 percent. The telephone poll of 1,111 registered voters was taken Nov. 16-20.